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Evolutionary Game Theory: A Generalization of the ESS Definition

Author

Listed:
  • Elvio Accinelli

    (Universidad Autónoma de San Luis Potosí, à lvaro Obregón #64, Col. Centro, C. P. 78000, San Luis Potosí, S. L. P., Mexico)

  • Filipe Martins

    (Department of Mathematics, Faculdade de Ciências da, Universidade do Porto, Rua do Campo, Alegre, s/n, 4169-007 Porto, Portugal3Laboratório de Inteligência Artificial e, Apoio à Decisão (LIAAD), INESC TEC, Campus da FEUP, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal)

  • Jorge Oviedo

    (Instituto de Matemática Aplicada San Luis, Universidad Nacional de San Luis, Ejército de los Andes 950, 5700 San Luis, Argentina5Consejo Nacional de Investigaciones, Científicas y Técnicas (CONICET), Ejército de Los Andes 950 5700, San Luis, Argentina)

Abstract

In this paper, we study the concept of Evolutionarily Stable Strategies (ESSs) for symmetric games with n ≥ 3 players. The main properties of these games and strategies are analyzed and several examples are provided. We relate the concept of ESS with previous literature and provide a proof of finiteness of ESS in the context of symmetric games with n ≥ 3 players. We show that unlike the case of n = 2, when there are more than two populations an ESS does not have a uniform invasion barrier, or equivalently, it is not equivalent to the strategy performing better against all strategies in a neighborhood. We also construct the extended replicator dynamics for these games and we study an application to a model of strategic planning of investment.

Suggested Citation

  • Elvio Accinelli & Filipe Martins & Jorge Oviedo, 2019. "Evolutionary Game Theory: A Generalization of the ESS Definition," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 21(04), pages 1-19, December.
    • Handle: RePEc:wsi:igtrxx:v:21:y:2019:i:04:n:s0219198919500051
    DOI: 10.1142/S0219198919500051
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    Cited by:

    1. William C. Grant, 2023. "Correlated Equilibrium and Evolutionary Stability in 3-Player Rock-Paper-Scissors," Games, MDPI, vol. 14(3), pages 1-16, May.
    2. Yanwei You & Yuquan Chen & Yujun You & Qi Zhang & Qiang Cao, 2023. "Evolutionary Game Analysis of Artificial Intelligence Such as the Generative Pre-Trained Transformer in Future Education," Sustainability, MDPI, vol. 15(12), pages 1-12, June.

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